Question

Suppose X is a random variable with expected value 260 and standard deviation 120, and Y is a random variable with expected value 170 and standard deviation 70. Compute each of the means and standard deviations indicated below (round off your answers to two decimal places, if necessary).

E(1.7X)=

SD(1.7X)=

SD(X+Y)=

E(X−Y)=

SD(X−Y)=

Now let Y1 and Y2 be two instances of the random variable YY and
compute the following (again, rounding to two decimal places, if
necessary).

E(Y1+Y2)=

SD(Y1+Y2)=

E(Y1−Y2)=

SD(Y1−Y2)=

Answer #1

Given independent random variables with means and standard
deviations as shown, find the mean and standard deviation of each
of these variables:
Mean
SD
a) 4X
b) 4Y+3
c) 2X+5Y
X
70
14
d) 5X−4Y
e) X1+X2
Y
10
5
a) Find the mean and standard deviation for the random variable
4X.
E(4X)=_____________
SD(4X)=_______________
(Round to two decimal places as needed.)
b) Find the mean and standard deviation for the random variable
4Y+3.
E(4Y+3)= ________________
SD(4Y+3)= _____________________
(Round to...

Suppose that X is a random variable with mean 21 and standard
deviation 4 . Also suppose that Y is a random variable with mean 42
and standard deviation 8 . Find the mean of the random variable Z
for each of the following cases
(Give your answer to three decimal places.)
a) Z = 3 + 10X
b) Z = 3X − 10
c) Z = X + Y
d) Z = X − Y
e) Z = −4X...

Suppose X is a Normal random variable with with expected value
31 and standard deviation 3.11. We take a random sample of size n
from the distribution of X. Let X be the sample mean. Use R
to determine the following:
a) What is the standard deviation of X when n =
19?
b) What is the probability that X1 + X2 +
... +X20 > 630?
PLEASE ANSWER IN R SCRIPT

Suppose X is a random variable with with expected value -0.01
and standard deviation σ = 0.04.
Let
X1,
X2, ...
,X81
be a random sample of 81 observations from the distribution of
X.
Let X be the sample mean. Use R to determine the
following:
Copy your R script
b) What is the approximate probability that
X1 +
X2 + ...
+X81 >−0.02?

The expected values, variances and standard Deviatiations for
two random variables X and Y are given in the following table
Variable
expected value
variance
standard deviation
X
20
9
3
Y
35
25
5
Find the expected value and standard deviation of the following
combinations of the variable X and Y. Round to nearest whole
number.
E(X+10) = ,
StDev(X+10) =
E(2X) = ,
StDev(2X) =
E(3X-2) = ,
StDev(3X-2) =
E(3X +4Y) = ,
StDev(3X+4Y) =
E(X-2Y) = ,
StDev(X-2Y) =

A random variable X is exponentially distributed with an
expected value of 33.
a-1. What is the rate parameter λ? (Round your answer to 3
decimal places.)
a-2. What is the standard deviation of X?
b. Compute P(23 ≤ X ≤ 43). (Round intermediate calculations to
at least 4 decimal places and final answer to 4 decimal
places.)
c. Compute P(20 ≤ X ≤ 46). (Round intermediate calculations to
at least 4 decimal places and final answer to 4 decimal...

A random variable X is exponentially distributed with
an expected value of 57.
a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of
X?
b. Compute P(54 ≤ X ≤ 60).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
c. Compute P(45 ≤ X ≤ 69).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal...

From the probability distribution given below, find the mean,
variance, standard deviation and expected value of the random
variable, X. Round your values for variance and standard deviation
to two decimal places (if necessary).
X
27
32
54
63
78
P(X)
5/18
1/4
1/12
2/9
1/6

Question 7) Suppose X is a Normal random variable with with
expected value 31 and standard deviation 3.11. We take a random
sample of size n from the distribution of X. Let X be the sample
mean. Use R to determine the following:
a) Find the probability P(X>32.1):
b) Find the probability P(X >32.1) when n = 4:
c) Find the probability P(X >32.1) when n = 25:
d) What is the probability P(31.8 <X <32.5) when n =
25?...

Random variable X has mean 16 and standard deviation 9, random
variable Y has mean 12 and standard deviation 7, the correlation
between X and Y is 0.3.
How can we find the correlation between 4X - 5Y and 3Y - 1.

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